(CNN) -- Florida Gov. Jeb Bush would be "awfully good" in the job of president, but the timing isn't right, his father and former President George H.W. Bush told CNN Tuesday.

Asked if he would want Jeb to run, Bush said, "Someday I would, yes."

Bush, who was president from 1989-1993, appeared on CNN's "Larry King Live" with former first lady Barbara, from the family compound in Kennebunkport, Maine.

Jeb Bush is in his second gubernatorial term, which ends in January 2007. His brother George ends his second presidential term in January 2009 and cannot run again.

"He'd be awfully good," the elder Bush said. "This guy's smart, big and strong. Makes the decisions. And you know, not without controversy, but he's led that state."

But the former president, who turns 81 this month, said, "The timing's wrong. The main thing is, he doesn't want to do it."

But he added, "Nobody believes that."

Jeb and George W. are two of six children by George and Barbara Bush; one died in childhood.

Bush on Clinton

The current President Bush asked his father and former Democratic President Bill Clinton to raise money for those hard hit by the tsunami in southern Asia late last year.

The elder Bush described the devastation as "terrible" and said the shared assignment has brought the two former presidents closer.

"No question about it. And Larry, you feel you're doing something bigger than your own political lives or bigger than your own self. I mean, what we saw out there -- and I'm anxious to see him when he gets back about this, what he's seen recently -- it just breaks your heart -- particularly the children. And he's been good to work with."

Bush said progress is being made to reconstruct the area, but "there's a long way to go."

The Bush-Clinton Fund has raised about $12 million from Americans, he said, and Clinton planned to visit Kennebunkport this month.

Asked whether he considered Clinton a friend, the elder Bush replied, "Well, as far as I'm concerned, it is a friendship. And you know, Larry, there's a perception that if you run against somebody, you're enemies. Well, Bill Clinton and I were not enemies."

"When I was president, he was the Democrat governor in charge of the educational summit. He headed it up for the Democratic governors. We worked very closely together."

"I just enjoy being with the guy. And he is very considerate of me. I'm, you know, old enough to be his dad," Bush added.

Barbara Bush was less enthusiastic.

"You heard what Bill Clinton said?" the former first lady asked. "When -- when I jokingly referred to him as 'son,' and he said, a good Democrat friend of his said, 'Those Bushes will do anything to get another president in the family.'"

Barbara Bush said she liked Clinton, then appeared to change her mind -- but didn't finish her sentence. Her husband quickly added, "However, she hasn't been around him."

Barbara Bush added that she appreciated the fact that Clinton has not criticized her presidential son.

Her birthday is four days before her husband's.

Bush made two parachute jumps over his presidential library in College Station, Texas, as part of his 80th birthday celebration. As a young Navy pilot during World War II Bush had to bail out of his plane after it took enemy fire. He also made a jump in March.

"I want to be alive in 2008 when the George H.W. Bush, the latest nuclear carrier, is christened," said Bush. "I want to be on the bridge. I can do it."

"I got to make another parachute jump in 2009."

Other political musings

On the political front, Bush said he hopes the controversial nominee John Bolton is confirmed as U.S. ambassador to the United Nations when the Senate reconvenes after a weeklong recess.

"I think he ... he's very knowledgeable, very bright, and that's what the president feels, and that's what the top people around the president feel."

Bush also criticized Amnesty International for condemning the United States for what it called "serious human rights violations" at Guantanamo Bay.

"That's ridiculous. And I'm inclined to agree with Gen. [Richard] Myers, the chairman of the Joint Chiefs, who's the most honorable of officers" that that isn't the case.